I am not American, so bear that in mind as you read my response to this question. Firstly, I agree with your lecturer when he says that rights are not "given" by a government or country. They are indeed given by God, which means it is the government's responsibility to uphold those rights and ensure their fulfilment. However, at the same time, there is always a sense in which the general situation of inequality and poverty that plagues every country is going to mean that those rights are more available for some than for others. To what extent, for example, can a single woman working three jobs and trying to look after her children at the same time be said to be able to engage in the pursuit of her own happiness?
This points towards the way in which the achievement of having those rights for everybody is something of a partial process, in that it is not completed as yet. Governments and administrations, if they are doing their job properly, should be trying to introduce new legislation to make their society more equitable and therefore give a greater chance for these rights to actually be equally available among their populace. Unfortunately, because we are humans and we make lots of mistakes thanks to our personal greed, this is something that has to be an ongoing process. Does this begin to answer your question?